As part of my teacher training, I'm taking a course in math methods, which means it's teaching me how to teach math. One thing I learned in this class this very week is a math lesson should be built around a math problem. We as teachers are not to start a math class by teaching a procedure like, say, subtraction, then have the kids practice the procedure, and then give them a word problem about two cars that start at different times but ending up in the same place at the same time, a problem which would probably require the procedure known as multiplication to solve, not subtraction, but you get my point. (By the way, procedures like addition, subtraction, multiplication and division are apparently called "algorithms." I thought an algorithm was a very fancy and long sequence of calculations that told you things like how much protein is in your blood when you're pregnant and how populations tend to move over time, but I was wrong.)
In any case, organizing a math lesson by putting the procedure/algorithm first is apparently not so good. It was how the math lessons I was taught were organized, and since I remember almost none of the math I was taught, I can't argue that teaching this way works well. (Please don't ask how I'm going to teach math if I don't remember any of it. I'm working on that.)
The alternative to the procedure-first lesson plan is the problem-first plan. Here's how it goes. First, you introduce a problem. Next, you explain to the kids what they need to do (set up the problem) but not how they need to do it. Then, let them work it out. When they're done working it out (or as done as they're going to get), talk about they're solutions as a group. (Eventually, they'll practice the procedure, or their own variant of it, to get more proficient.)
Now, except for the talking instead of eating, doesn't that sound pretty much exactly like a quickfire challenge? I suspect that quickfires might be the perfect model for the problem-first lesson plan. I don't know this for sure, since I've yet to plan a lesson, but it's possible. After all, if reality shows can serve up life lessons, why not lesson plans?